course slides jan 05 2015(1)
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Copyright @ Samir H. Mushrif
Samir H [email protected]
http://www.ntu.edu.sg/home/shmushrif/
Division of Chemical and Biomolecular Engineering
School of Chemical and Biomedical Engineering
Nanyang Technological University, Singapore
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Suraj [email protected]
Division of Chemical and Biomolecular Engineering
School of Chemical and Biomedical Engineering
Nanyang Technological University, Singapore
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4Samir H Mushrif (7) Suraj Vasudevan (6) Introduction to Unit Operations/Separation
Processes
Fundamentals
Phase Equilibria/Diagrams
Thermodynamics of Phase Equilibria
Modeling Phase Equilibria
Distillation
Flash Distillation
Column Distillation
Advanced Binary Distillation
Multicomponent Distillation
Absorption and Stripping
Liquid – Liquid Extraction
Mass Transfer Equipment – Design and
Operation Mass Transfer Analysis
Separation using Membranes
Adsorption and Chromatography
Aspen – HYSYS
All the exams and quizzes will be open book type (Wankat Textbook, handwritten class
notes and Slides only. NO laptops, netbooks, ipads, palmtops, smartphones, tablets)
Final Exam (5060%)
25 30% on Fundamentals and Distillation (Samir)
25 30% on Other Separation Processes (Suraj)
Two quizzes/midterms (35 45% combined)
First on Fundamentals and Distillation (Samir)
Second on Other Separation Processes (Suraj)
Assignments (Upto 5%)
What if you miss a quiz?
Can take it again, but the next
one will be harder.
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5
Textbook
• Separation Process Engineering . Phillip C. Wankat, 2nd/3rd Edition, Prentice
Hall, New Jersey. Other Reference Books
• Seader, J.D and Henley, E.J. (1998) New Jersey, Separation Process
Principles, 3rd Edition, John Wiley, 2010
• Cussler E.L, Diffusion; Mass Transfer in Fluid Systems, end Ed. New York:
Cambridge University Press, 3rd Edition, 1997• McCabe, W.L. Smith, J.C. and Harriot P, Unit Operations of Chemical
Engineering, 7th Edition, Singapore: McGraw-Hill, (2005)
• Treybal, R.E. (1981), Mass-Transfer Operations, 3rd Edition, Singapore:
McGraw-Hill
• Perry, RH, Green DW, Perry’s Chemical Engineers’ Handbook, 8th Edition,
McGraw-Hill – Available Online (2008)
Recommended Books
How to read a Unit Operations book?
Page no. X to Page no. Y or Look for the concepts
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6
Please attend lectures and tutorials and browse previous lecture notes before you come
for a class. Learning in a class is a lot easier than self –study.
Every lecture is like a step in the ladder. If you miss a step, you may have problem
climbing the next (We will do a brief review at the beginning). You may forget the equations, but not the concepts
Silence in the classroom please. Time will be given for discussion.
Active class participation is strongly encouraged. Ask questions. I shall be in the lecture
theatre 2530 mins. before the lecture begins. Even after the class/tutorial is okay.
Please don’t use laptops, smartphones, ipads etc. in the classroom
Please take notes during the class. Slides only give an overview.
Solve problems and read books. Solve problems to develop your “application” skills; not
because one of them will be in the exam! Watching lecture videos or reading slides is
not sufficient.
Don’t delay your studies till the very last minute
General Recommendations and Policy
Open door policy (N1.2 –B2 –23). 2 hrs. every week for consultation (Let’s decide thetime now!). Come in groups, if possible.
Asking conceptual questions by email … may not be a good idea!
NO consulting 3 days before the exam
Video recording of lectures and slides on the web. Will rerecord, if needed.
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8Where does this course fit into your curriculum?
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9Course Objectives
To learn about different separation processes commonly employed
in industries.
To understand the fundamentals behind these processes and theoperation of separation equipments.
To understand how operating conditions, equipment design and
process variables can affect the separation
To be able to control a process, you have to know the processinside –out
To be able to design some of the most important unit operations like
distillation
Use the state of the art computational tools for design and analysis
of unit operations
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10Learning Outcome (Take a look at this slide at the end of the semester )
At the end of the course, you should
Have a list of some of the key separation processes employed in the
industry Be able to read and interpret the thermodynamic data (in the form of
Temperature –Pressure –Composition Diagrams)
Be able to use the data to decide the type of separation method to be
employed
Be able to design single stage processes
Be able to explain how single stage processes can be combined in an
efficient manner to form cascades
Be able to use graphical, mathematical and computational tools to design
countercurrent separations
Be able to design multicomponent systems using HYSYS
Build a strong foundation which will prepare you to learn advanced
separation processes and to handle complications in actual
implementation of these processes
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12Separations in a Chemical Plant (> 50% of the capital and operating costs)
www.ontime.methanetomarkets.org
Oil Refinery Demonstration
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13History of Unit Operations and Chemical Engineering
Arthur D. Little William H. Walker Warren K. Lewis
Pictures from MIT and ACS websites
“Chemical Engineering” as a distinct profession. Difference between a chemical
engineer and a chemist.
Arthur D. Little coined the term “Unit Operation”
William H. Walker and Arthur D. Little formed a company and later Walker returnedto MIT
Warren K Lewis, the first head of the chemical engineering department at MIT
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14Mixing vs. Separation
What is spontaneous, MIXING or SEPARATION? And why?
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15Mixing vs. Separation
What is spontaneous, MIXING or SEPARATION? And why?
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16Mixing vs. Separation
What is spontaneous, MIXING or SEPARATION? And why?
S T H G
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17Mixing vs. Separation
What is spontaneous, MIXING or SEPARATION? And why?
S T H G 1. Change in free energy has to be +ve or –ve?
2. How does the entropy of the system change upon mixing?
3. What is ∆H related to?
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18Mixing vs. Separation
What is spontaneous, MIXING or SEPARATION? And why?
S T H G 1. Change in free energy has to be +ve or –ve?
2. How does the entropy of the system change upon mixing?
3. What is ∆H related to?
Water and alcohol mix at room temperature
Oil and water do not mix at room temperature
Oil and water may mix at a higher temperature
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19Types of Separation
Distillation
Evaporation
Extraction
Crystallization
Drying
Absorption
OsmosisFiltration
Dialysis
Pervaporation
Adsorption
Ion – Exchange
Centrifugation
Electrolysis
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20How to select a separation process?
Feed and Product Conditions
• Concentration of the species to be removed
• Flowrate of the feed
• Temperature, Pressure
• Physical State of the feed (Solid, liquid, gas)
Property Differences amongst the Components
• Molecular• Thermodynamic
• Transport
Characteristics of the Operation
• Ease of Scale – up
• Energy requirement
• Size Limitations
• Temperature, Pressure and Physical state requirements
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21Three important questions to ask for separations
Will it happen? If yes, how much?
Equilibrium
How fast?
Kinetics
Sodium Chloride Video
mequilibriu K RT G ln
F r e e
E n e r g y
F r e e
E n e r g y
RT E a
Aek
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22Separations vs. Reactions
Typical Properties
• Chemical potential, equilibrium
coefficient, saturation capacity etc.
Reaction Equilibrium analogous to Separation Equilibrium and Reaction Kinetics
analogous to Separation Kinetics
Typical Properties
• Mass transfer coefficient, Diffusion
coefficient (Diffusivity)
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23Separations vs. Reactions
Typical Properties
• Chemical potential, equilibrium
coefficient, saturation capacity etc.
Reaction Equilibrium analogous to Separation Equilibrium and Reaction Kinetics
analogous to Separation Kinetics
Typical Properties
• Mass transfer coefficient, Diffusion
coefficient (Diffusivity)
Water + Dimethyl Sulfoxide
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24What controls the separation processes?
Many of the separation processes are equilibrium limited.
Thermodynamic equilibrium data is crucial for the design of aseparation process
Mathematical description of the underlying phenomenon is equally
important
For polymers attracted to the surface,
there is no kinetic barrier but the
protein competes with the polymer for
adsorption sites. Polymers that are not
attracted to the surface present a large
steric barrier but not very good
thermodynamic prevention because ofthe ability of the protein to deform the
polymer layer.Satulovsky J et al. PNAS 2000;97:9037-9041
25
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26
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26Thermodynamic Equilibrium
Thermal Chemical Mechanical
Temperatures are
the same
Chemical potentials
are the same
Pressures are the
same
Phase Equilibria
(Phase Creation and Phase Addition type Separation Processes – Distillation)
The equilibrium relationships between phases (such as vapor, liquid, solid) of a chemical
compound or mixture under various conditions of temperature, pressure, and composition McGraw Hill Science and Technology Dictionary
Water and Steam in equilibrium at 100 C and 1 atm. pressure
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27Phase Diagram of Water (Single Component)
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28Critical Point of Water
SupercriticalConditions
http://www.science.uva.nl/research/mgrd/video-cp.html
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29Phase Diagram for a Binary System
Mass Transfer Operations – Treybal
Now composition comes into picture!
30
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30Gibb’s Phase Rule
2 P C F
Degrees of Freedom Number of Components Number of Phases
Examples
• How many triple points can be there for water?
• What are the maximum number of phases in a binary mixture?
Liquid
A
Liquid
B
Vapor
A
Vapor
B Number of components = C (i , j, k, …, C )
Number of phases = P (α, β, γ, …, P )
Temperatures = T α , T β , T γ ,… T P
Pressures = pα , p β , pγ ,… p P
Chemical Potentials = μαi , μα j , μαk , … μαC
μ β i , μ
β j , μ
β k , … μ β
C
…
μ P i , μ
P j , μ
P k , … μ P
C
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31Gibb’s Phase Rule
Thermal
Chemical
Mechanical
Phase Equilibria: Thermal, Chemical and Mechanical Equilibria
Equations1...
P T T T
P
Equations1... P p p p P
Equations1
...
...
...
P
CCC
P j j j
P
iii
P C
phasestheallof PressureandeTemperatur
phasestheallincomponentsof FractionsMole
21variablesof numberTotal P C P
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32Gibb’s Phase Rule
2
1221
Equationsof Numbervariablesof NumberFreedomof Degrees
P C F
P C P C P F
This phase rule is applicable to non – reacting systems
The degrees of freedom correspond to the intensive variables like mole
fractions, pressure and temperature.
Once you select all your degrees of freedom, there exists a unique system.
C P F
1 1 2
1 2 1
1 3 0
33C f f
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33Concept of Vapor Pressure – In the context of VLE
What happens if I keep a bowl of water in open for 12 hrs. at 50 C
on a very hot summer day?
What happens if I keep a lid and cover the bowl?
What is the vapor pressure of water at 100 C?
34C t f V P I th t t f VLE
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34Concept of Vapor Pressure – In the context of VLE
What happens if I keep a bowl of water in open for 12 hrs. at 50 C
on a very hot summer day?
What happens if I keep a lid and cover the bowl?
What is the vapor pressure of water at 100 C?
35V Li id E ilib i (Si l t bi )
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35Vapor – Liquid Equilibria (Single component vs. binary)
Water boils at 100 C under 1 atm. Pressure
At 100 C, vapor pressure of water is equal to 1 atm.
D E
T e m p
e r a t u r e ( C )
q (KJ/kg)A
A
B
B
C
C
D
E
Subcooled
Water
Saturated
Water Only
Water and
Steam
SaturatedSteam Only
Superheated
Steam
How would this curve look at different pressures? Why?
How would this curve look if I have a water (100 C)+ ethanol (78.4 C) mixture?
What will be the boiling point of the mixture?
36V Li id E ilib i (Si l t bi )
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36Vapor – Liquid Equilibria (Single component vs. binary)
Single component VLE Binary VLE
Is the composition of the liquid and the vapor phase same?
If not, can you say something about the distribution? Justify your argument.
Vapor pressure of Water and Water + ethanol mixture same as atmospheric pressure
37V Li id E ilib i (Si l t bi )
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37Vapor – Liquid Equilibria (Single component vs. binary)
Single component VLE Binary VLE
Is the composition of the liquid and the vapor phase same?
If not, can you say something about the distribution? Justify your argument.
Vapor pressure of Water and Water + ethanol mixture same as atmospheric pressure
A binary mixture boils over a range of temperature and the liquid (andvapor) composition changes during the phase transition. Explain.
38Bi VLE Di (C t t P )
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38Binary VLE Diagram (Constant Pressure)
T e m p e r a t u r e ( C )
Mole Fraction of component “A” ( xA, yA)0 1
b
AT
b
BT
Liquid
Vapor
Bubble point
Curve
Dew point
Curve
Liquid + Vapor
xA=0.5
yA=0.81
39Wh t i th diff b t th t VLE di ?
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39What is the difference between these two VLE diagrams?
T e m
p e r a t u r e ( C )
Mole Fraction of component“A” ( xA, yA)
T e m
p e r a t u r e ( C )
Mole Fraction of component“A” ( xA, yA)
40What is the difference between these two VLE diagrams?
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40What is the difference between these two VLE diagrams?
T e m
p e r a t u r e ( C )
Mole Fraction of component“A” ( xA, yA)
T e m
p e r a t u r e ( C )
Mole Fraction of component“A” ( xA, yA)
A A
A A
A A
A A AB
y x
x y
x x
y y
1
1
1
1VolatlityRelative
41How would the Composition Curve for “A” ( ) look like?
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41How would the Composition Curve for “A” ( xA, yA) look like?
T e m
p e r a t u r e ( C )
Mole Fraction of component“A” ( xA, yA)
42How would the Composition Curve for “A” (x y ) look like?
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Mole Fraction of component“A” ( xA) in Liquid
M o l e F r a c
t i o n o f c o m p o
n e n t
“ A ”
( y A
) i n V a p o r
A x
A y
T e m
p e r a t u r e ( C )
Mole Fraction of component“A” ( xA, yA)
A x A y
How would the Composition Curve for “A” ( xA, yA) look like?
43How would the Enthalpy Composition Curve look like?
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How would the Enthalpy –Composition Curve look like?
T e m p e
r a t u r e ( C )
Mole Fraction of component
“A” ( xA, yA)
44How would the Enthalpy Composition Curve look like?
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How would the Enthalpy –Composition Curve look like?
T e m p e
r a t u r e ( C )
Mole Fraction of component
“A” ( xA, yA)
E n t h a l p y ( K J / m o l )
Mole Fraction of component
“A” ( xA, yA)
45How would the Pressure Composition Curve look like?
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How would the Pressure –Composition Curve look like?
T e m p e
r a t u r e ( C )
Mole Fraction of component
“A” ( xA, yA)
46How would the Pressure Composition Curve look like?
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How would the Pressure –Composition Curve look like?
T e m p e
r a t u r e ( C )
Mole Fraction of component
“A” ( xA, yA)
P r e s s u r e ( a t m . )
Mole Fraction of component
“A” ( xA, yA)
47Boiling of a Binary Mixture at Constant Pressure
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Boiling of a Binary Mixture at Constant Pressure
T e m p e r a t u r e ( C )
Mole Fraction of component “A” ( xA, yA)0 1
b
AT
b
BT
Liquid
Vapor
Bubble point
Curve
Dew point
Curve
L
V
L
A x
V
A y
?andaboutsayyoucanWhat V
A
L
A y x
How do I travel on the composition curve if I transform a liquid of composition “x LA” completely to vapors?
48Boiling of a Binary Mixture at Constant Pressure
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Boiling of a Binary Mixture at Constant Pressure
T e m p
e r a t u r e ( C )
Mole Fraction of component “A” ( xA, yA)0 1
b
AT
b
BT
Liquid
Vapor
Bubble point
Curve
Dew point
Curve
L
V
L
A x
V
A y
V
A
L
A
V
A
L
A y x y x ?andaboutsayyoucanWhat
49Boiling of a Binary Mixture at Constant Pressure
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Boiling of a Binary Mixture at Constant Pressure
T e m p
e r a t u r e ( C )
Mole Fraction of component “A” ( xA, yA)0 1
b
AT
b
BT
Liquid
Vapor
Bubble point
Curve
Dew point
Curve
L
V
L
A x
V
A y
1 B1 D
1 B
A x
1 D
A x
Tie Line
50Boiling of a Binary Mixture at Constant Pressure
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Boiling of a Binary Mixture at Constant Pressure
T e m p
e r a t u r e ( C )
Mole Fraction of component “A” ( xA, yA)0 1
b
AT
b
BT
Liquid
Vapor
Bubble point
Curve
Dew point
Curve
L
V
L
A x
V
A y
1 B2 B
1 D
2 D
2 B
A x
2 D
A x
51Boiling of a Binary Mixture at Constant Pressure
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Boiling of a Binary Mixture at Constant Pressure
T e m p
e r a t u r e ( C )
Mole Fraction of component “A” ( xA, yA)0 1
b
AT
b
BT
Liquid
Vapor
Bubble point
Curve
Dew point
Curve
L
V
L
A x
V
A y
1 B2 B
3 B
1 D
2 D
3 D
3 B
A x
3 D
A x
52Mass balance for the two phases
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Mass balance for the two phases
T e m p e r a t u r e ( C )
Mole Fraction of component “A” ( xA, yA)0 1
b
AT
b
BT
Liquid
Vapor
Bubble point
Curve
Dew point
Curve
L
V
L
A x
V
A y
1 B2 B 1 D
2 D E
phases?)(vaporand)(liquidof amountsrelativethe bewhat would
, pointreachesittillheatedisncompositiowithfeedof molesIf
V L
E x F L
A
2 B
A x
2 D
A x
53Lever – Arm Rule
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Lever Arm Rule
2of length
2of length
get,we(b)Equationinto(a)equationfromngSubstituti
(b)
: balanceMaterialA""Component(a)
: balanceMaterialOverall
2
2
22
22
EB
ED
V
L
x x L x xV
F
Vx Lx Fx
V L F
L A B A
D A
L A
x x
x x
L
A
B
A
D
A
L
A
D
A
B
A
L
A
54
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55Thermodynamics of Phase Equilibria
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Thermodynamics of Phase Equilibria
Thermal Chemical Mechanical
Temperatures are
the same
Chemical potentials
are the same
Pressures are the
same
Phase Equilibria
(Phase Creation and Phase Addition type Separation Processes – Distillation)
The equilibrium relationships between phases (such as vapor, liquid, solid) of a chemical
compound or mixture under various conditions of temperature, pressure, and composition McGraw Hill Science and Technology Dictionary
What is Chemical Potential? And Why does it have tobe equal for a component in all phases at equilibrium?
56Equality of Chemical Potentials
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Equality of Chemical Potentials
V
B
L
B
V
A
L
A
B
V
B A
V
A B
L
B A
L
A
B
V
B B
L
B A
V
A A
L
A
B
nT P B
A
nT P AnnT nn P
B A
Vyd Vyd Lxd Lxd
Vyd Lxd Vyd Lxd dG
G P T
dnn
Gdn
n
GdP
P
GdT
T
GdG
B A
P T G
nn P T f G
B
A
A
B B A B A
and
0
)(minmequilibriuatissystemwhen the,and particular aAt
andcomponentsof amounts
and,inchangessmalltodueinchangeThe
,,,
,,,,,,,,
57Do I have a “chemical potential meter”?
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p
""componentof fugacitytheis
lngasidealanlike behaveseverythingnotBut
ln
componentinchangetodueis pressureinchangetheIf
pressureof in terms
potentialChemical
can writewegasidealanFor
mics,ThermodynaFrom
,,,
,,,
2
i f
f RTd d
P RTd d
i
P P
RT
n
V
P
RT nV
P n
V
n P
G
i
ii
ii
nT
i
in P T ii
i
nT
i
n P T ii
j j
j j
58VLE in terms of “Fugacity”
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g y
V
i
L
i f f
m,EquilibriuLiquid-VaporAt
Fugacity is something like “pressure”
Single component VLE
Water and Steam in equilibrium at 100 C – Vapor pressure of water and
(partial) pressure of steam are equal
P yVP x wwW
59VLE in terms of “Fugacity”
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g y
V
i
L
i f f
m,EquilibriuLiquid-VaporAt
Fugacity is something like “pressure”
Binary VLE
Vapor and Liquid phases of water and ethanol in equilibrium at T C, VP of
the system equal to P (Ideal gas and Ideal Liquid)
P yVP x iii
60VLE in terms of “Fugacity” (non – ideal systems)
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g y ( y )
Where does the non – ideality for gases and liquids come
from?
61VLE in terms of “Fugacity” (non – ideal systems)
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g y ( y )
tcoefficienfugacity
statestandardatfugacitycomponent pure
tcoefficienactivity
where
aswritten becanequationAbove
m,EquilibriuLiquid-VaporAt
0
i
0i
i
i
iiii
V
i
L
i
f
P y f x
f f
Where does the non – ideality for gases and liquids come
from? – Intermolecular Forces
62How to calculate these coefficients?
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Liquid Phase Gas Phasei tCoefficienActivity i tCoefficienFugacity
van Laar
NRTL
UNIQUAC
UNIFAC
Margules
Van der Waals EOS
Redlich – Kwong (RK)
Peng – Robinson (PR)
Elliott, Suresh, and Donohue
(ESD)
63VLE of an ideal system (Ideal Liquid and Ideal Gas)
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tCoefficienonDistributi
LawsRaoult'calledalsoisequationaboveThe
1:GasIdealanFor
,1:LiquidIdealanFor
m,EquilibriuLiquid-VaporAt
0i
0i
ii
i
i
iii
i
ii
iiii
V
i
L
i
K P
VP
x
y
P yVP x
VP f
P y f x f f
64Binary Vapor Pressure Curve using Raoult’s Law
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P P y P yVP xVP x P yVP x
B A P
B
P
A B B A Aiii
B A A A VP xVP x P 1
Mole Fraction of component “A” ( xA)
P r e s s u r e
0 1
T
65Binary Vapor Pressure Curve using Raoult’s Law
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B A A A VP xVP x P 1
Mole Fraction of component “A” ( xA)
P r e s s u r e
0 1
T Can you calculate the “red
(P vs.y A)” curve?
66Binary Vapor Pressure Curve using Raoult’s Law
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B A A A VP xVP x P 1
Mole Fraction of component “A” ( xA)
P r e s s u r e
0 1
T
P
VP x y
P
VP x y
P
VP x y
P yVP x
B A A
B B B
A A A
A A A
11
????1
1
B
A
A A
A A
VP
VP
y x
x y
Can you calculate the “red
(P vs.y A)” curve?
67Binary Vapor Pressure Curve using Raoult’s Law
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B A A A VP xVP x P 1
Mole Fraction of component “A” ( xA)
P r e s s u r e
0 1
T
P
VP x y
P
VP x y
P
VP x y
P yVP x
B A A
B B B
A A A
A A A
11
B
A AB
B
A
A A
A A
K
K
VP
VP
y x
x y
VolatilityRelative
1
1
Can you calculate the “red
(P vs.y A)” curve?
68How to construct a T – xy diagram for an ideal system?
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C T
B AVP
x
x y
VP
VP
y x
x y
AB A
A AB A AB
B
A
A A
A A
log
:EquationAntoine
chartPriesterDeMethodsGraphical
EquationAntoine
data pressurevaporcomponent puretheisneedyouAll
111
1
Can you calculate the boiling point of Ethanol at 1 atm. if I give you
the Antoine Equation parameters?
69De Priester chart
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From Separati on Process Engi neeri ng, Thi rd Editi on by Phillip C. Wankat
(ISBN: 0131382276) Copyright © 2012 Pearson Education, Inc. All rights reserved.
70Binary y – x diagram for an ideal system (constant α)
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Mole Fraction of component
“A” ( xA) in Liquid
M o l e F r a c t i o n o f c o m p o n e
n t
“ A ” ( y
A ) i n V a p o r
A x
A y
Increasing α
71An interesting question
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Mole Fraction of component
“A” ( xA) in Liquid
M o l e F r a c t i o n o f c o m p o n e
n t
“ A ” ( y
A ) i n V a p o r
A x
A y
11
AB A
A AB A
x x y
Can you prove mathematically
that a ( y,x) curve defined by the
following equation (with
constant α AB) can not look like
the “blue”, “red” or “green”
curves shown in this figure?
72Bubble and Dew Point Calculation
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I have a mixture (liquid phase) of two components, A and B, with
mole fractions x A and x B , at pressure P . What is the bubble point of
the mixture?
OR
I have a mixture (vapor phase) of two components, A and B, withmole fractions x A and x B , at pressure P . What is the dew point of
the mixture?
Do not construct the entire (T, xy) diagram.
Antoine equation parameters are given and assume ideal mixture.
73Bubble and Dew Point Calculation
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iterate.not,If .1if Check5.
andfractions;mole phasevaportheCalculate4.
at, pressuresvaporcomponent puretheCalculate3.
asguessretemperatuinitialanTake2.
pressuregivenat the
andof pointsBoilingtheCalculate1.
B A
B B B
A A A
initial B A
B
B B
B
A Ainitial
B
B
B
A
y y
P
VP x y
P
VP x y
T VP VP
T xT xT
P
T BT A
74
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75Deviations from Ideal Behavior
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Mole Fraction of component “A” ( xA)
T o t a l P r e s s u r e
0 1
T
Mole Fraction of component “A” ( xA)0 1
T
BVP
AVP
T o t a l P r e s s u r e
BVP
AVP
What gives rise to non – ideality? – Intermolecular Forces
(Tendency of molecules to escape)
76+ve Deviation from Raoult’s Law
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Mole Fraction of component “A” ( xA
)
P r e s s u r e
0 1
T
BVP
AVP
A A A
A A A
A
A A
A A A A
V
A
L
A
VP x P y
P yVP x
VP f
P y f x
f f
A
0A
0A
1:GasIdealanFor
,1:LiquidIdealanFor
m,EquilibriuLiquid-VaporAt
idealisphasegasthe
andideal-nonisphaseliquidtheIf
)veislog(
)veislog(
idealityfromdeviationve:1γ
idealityfromdeviationve:1γ
A
A
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78Small Deviation vs. Large Deviation
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Mole Fraction of component “A” ( xA)
P r e s s u r e
0 1
T
BVP
AVP
Mole Fraction of component “A” ( xA)
P r e s s u r e
0 1
T
BVP
AVP
What is the difference when the deviations are large?
79Small Deviation vs. Large Deviation
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Mole Fraction of component “A” ( xA)
P r e s s u r e
0 1
T
BVP
AVP
Mole Fraction of component “A” ( xA)
P r e s s u r e
0 1
T
BVP
AVP
What is the difference when the deviations are large?
Is there a maximum in pressure? Do we have the same pressure for two
different compositions?
80P – xy Curves for Large Deviation from ideality
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Mole Fraction of “A” ( x A ,y A)
P r e s s u r e
0 1
Liquid (P vs. x A)
Vapor (P vs. y A)
81P – xy Curves for Large Deviation from ideality
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Mole Fraction of “A” ( x A ,y A)
P r e s s u r e
0 1
Liquid (P vs. x A)
Vapor (P vs. y A)
Can it look like this?Explain mathematically and physically.
82P – xy Curves for Large Deviation from ideality
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Mole Fraction of “A” ( x A ,y A)
P r e s s u r e
0 1
Liquid (P vs. x A)
Vapor (P vs. y A)
Can it look like this?Explain.
B B A A
B A B A A B A
B A B B B A A A
B B A
A
A A
A A A
B A
A
B A A A
x y x y
K K x x K y y
x K x K y x K y
K P
VP
P
VP
x
y K
P yVP x
VP VP
x
P P
VP xVP x P
,
1
and
FugacityVaporFugacityLiquid
ismequilibriuforconditionBut the
0then,inmaximumaisthereIf
1
BA
A
BA
BA
83P – xy Curves for Large Deviation from ideality
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Mole Fraction of “A” ( x A ,y A)
P r e s s u r e
0 1
Liquid (P vs. x A)
Vapor (P vs. y A)
Mole Fraction of “A” ( x A ,y A)
Liquid (P vs. x A)
Vapor (P vs. y A)
P r e s s u r e
What is the difference between these two curves? Explain using intermolecular forcesand thermodynamics Vapor – Liquid composition is the same for a particular composition
The more volatile component becomes a less volatile component
VP at a composition is more than the individual component vapor pressures
10
84T – xy and x – y Curves for Large Deviation from ideality
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Mole Fraction of “A” ( x A ,y A)
T e m p e r a t u r e
0 1
Liquid (P vs. x A)
Vapor (P vs. y A)
Mole Fraction of “A” in Liquid ( x A)
0 1 M o l e F r a c t i o
n o f “ A ” i n V a
p o r ( y A
)
Minimum Boiling Azeotrope – Constant Boiling Mixture
85-ve Deviation from Ideality
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Mole Fraction of component “A” ( xA)
P r e s s u r e
0 1
T
BVP
AVP
A c t i v i t y C o e f f
. γ
A / B
0 1Mole Fraction of component “A” ( xA)
1 B
A
What will be the boiling point of an azeotrope of a mixture which
shows large – ve deviations from ideality?
86P – xy Curves for Large –ve Deviation from ideality
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Mole Fraction of “A” ( x A ,y A)
P r e s s u r e
0 1
Liquid (P vs. x A)
Vapor (P vs. y A)
Mole Fraction of “A” ( x A ,y A)
Liquid (P vs. x A)
Vapor (P vs. y A)
P r e s s u r e
10
What is the difference between these two curves? Explain using intermolecular forcesand thermodynamics Vapor – Liquid composition is the same for a particular composition
The more volatile component becomes a less volatile component
VP at a composition is less than the individual component vapor pressures
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88Partial Miscibility – Heteroazeotropes (Large +ve deviations)
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Mole Fraction of “A” ( x A ,y A)
T e m p e r a t u r e
0 1
Liquid
(T vs. x A)
Vapor (T vs. y A)
Mole Fraction of “A” in Liquid ( x A)
0 1 M o l e F r a c t i o
n o f “ A ” i n V a
p o r ( y A
)
A
B
C
A
B C
How will the VLE composition look like when you are in the 2 –
phase region?
89Partial Miscibility – Heteroazeotropes (Large +ve deviations)
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Mole Fraction of “A” ( x A ,y A)
T e m p e r a t u r e
0 1
Liquid
(T vs. x A)
Vapor (T vs. y A)
Mole Fraction of “A” in Liquid ( x A)
0 1 M o l e F r a c t i o
n o f “ A ” i n V a
p o r ( y A
)
A
B
C
A
B C
A* C*B*
2 Liquids
90Partial Miscibility – Heteroazeotropes (Large +ve deviations)
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Mole Fraction of “A” ( x A ,y
A)
T e m p e r a t u r e
0 1
Liquid
(P vs. x A)
Vapor (P vs. y A)
Mole Fraction of “A” in Liquid ( x A
)0 1 M
o l e F r a c t i o
n o f “ A ” i n V a
p o r ( y A
)
Why “Heteroazeotropes” are Minimum Boiling Azeotropes?
Why does the liquid phase split at lower temperatures?
91Some examples
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Ideal Mixture
• Hexane + Heptane, Benzene + methyl benzene, 1-propanol +
2-propanol
Positive Deviation from Raoult’s Law
• Water + Ethanol (minimum boiling azeotrope)
• CS2 + Acetone (minimum boiling azeotrope)
Negative deviation from Raoult’s Law
• Chloroform + Acetone (maximum boiling azeotrope)
• Water + Nitric Acid (maximum boiling azeotrope)
Heteroazeotropes Isobutanol + Water at 1 atm.
92
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93Basic Principle of Distillation (Reduce the pressure)
z
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P 1
P 2
z
x y
D
F E
T
T P z F ,,, 1
T P x L ,,, 2
T P yV ,,, 2
Liquid
Vapor
94Basic Principle of Distillation (Increase the temperature)
z
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1,,, T P z F
2,,, T P x L
2,,, T P yV
T 1
T 2
z
x y
D F E
P
Liquid
Vapor
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96Continuous Flash (Single Stage) Distillation
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Which variable can be specified?
QV
L
T
x
y
drum
:suppliedheatof Amount.6 :feedtheof portionVapor5.
:feedtheof portionLiquid.4
:drumflashtheof eTemperatur 3.
:fractionmole phaseLiquid.2
:fractionmole phaseVapor.1
How will the solution procedure be different if
I specify one of the first 5 variables vs.
I specify Q
97Continuous Flash (Single Stage) Distillation
Whi h i bl b ifi d?
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Which variable can be specified?
Q
F
V f V
F
Lq L
T
x
y
drum
:suppliedheatof Amount.6
:feedtheof portionVapor5.
:feedtheof portionLiquid.4
:drumflashtheof eTemperatur 3.
:fractionmole phaseLiquid.2
:fractionmole phaseVapor.1
How will the solution procedure be different if
I specify one of the first 5 variables vs.
I specify Q
Material and Energy Balance equations are independent
Material and Energy Balance equations are interdependent
98If T drum is specified …
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T drum
x y
F E
Liquid
Vapor
Look into your (T, xy)
diagram and find out the x
and y at the temperatureT drum
After finding x and y, solve
the material balance
equations (overall and
component) to calculate L
and V
Solve the energy balance
equation to get Q
99Graphical solution vs. Numerical Solution
Ideal case Raoult’s Law (Sequential)
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Ideal case – Raoult’s Law (Sequential)
Non – ideal case (Iterative)
equations balanceenergyandmaterialSolvent.3
Calculate2.
EquationsAntoine'ordataVPusingat pressurevaporGet the1.
Kx y P VP K
T
drum
drum
procedureiterativey Numericall3.
ncompositioof functionaisand 2.
EquationsAntoine'ordataVPusingat pressurevaporGet the1.
drum
drum
P
VP K
T
100If x or y is specified …
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T drum
x y
F E
Liquid
Vapor
Look into your (T,xy)
diagram and find out the
T drum corresponding to the x or y
Find the corresponding x or y
After finding x and y, solve
the material balance
equations (overall and
component) to calculate L
and V
Solve the energy balance
equation to get Q
101If f (V/F ) or q (L /F ) is specified …
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ploton the linestraightarepresentsequationThis
1
1
1
of in termsor
11
balance,materialcomponenttheFrom
x,y
z q
xq
q y
q
z f
x f
f y
V F L
z V
F x
V
L yVy Lx Fz
x
y
One of these points is my solution!
But, which one?
f
f 1Slope
y = x = z
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103What if I have more than 2 components? (Let’s say 3 …)
: PTPHzzFGiven
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11
21
,
,,,
T P
H z z F f
Q drum
drum
T
P
v H y yV ,,, 21
L H x x L ,,, 21
freedomof degree
singlealeft withstillareWe
Equations3
1
3
8,,,,,,,:
,,,,,,:
222
111
2211
1121
iii
LV f
drum
drum f
x K y
LH VH Q FH
Vy Lx Fz
Vy Lx Fz
V L F
T y x y xV LQ
P T P H z z F
RelationsmEquilibriu
BalanceEnergy
component)and(OverallBalanceMaterial
Unknowns
Given
104Multicomponent Flash Distillation
,,,,...,,,: 1121 drumf P T P H z z F Given
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11
21
,
,...,,,
T P
H z z F f
Q drum
drum
T
P
v H y yV ,...,,, 21
L H x x L ,...,,, 21
Freedomof degreeoneleft withstillareWe
21and1
Equations
1
24,...,,,,,,,:
,,,, ,,,
11
111
222
111
2211
1121
C
i
i
C
i
i
iii
LV f
C C C
drum
drum f
y x
x K yC
LH VH Q FH
C
Vy Lx Fz
Vy Lx Fz
Vy Lx Fz
V L F
C T y x y xV LQ
RelationstricStoichiome
RelationsmEquilibriu
BalanceEnergy
component)and(OverallBalanceMaterial
Unknowns
105
theallhaveyou willsystemidealanAssuming K
If T drum is specified …
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solved becan balanceenergythe
andobtained becan,,,,gettingAfter
MethodRaphson- Newtonusingsolved becanequationAbove
011
1
111
and111
11 and
11
;and
aswritten becanequationsmEquilibriuandequations balancematerialThe
theallhaveyou willsystem,idealanAssuming
1
1
11
V L y x f
f g
f g
f f
f g f K
z K
f K
z K
f K
z
f K
z K y
f K
z x
x K yVy Lx Fz V L F
K
ii
n
n
nn
C
i i
ii
C
i i
iiC
i i
i
i
iii
i
ii
iiiiii
i
106What if more separation is desired?
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11,
,,
T P
H z F f
Q drum
drum
T
P
v H yV ,,
L H x L ,,
z
What can I do to achieve this separation?
107
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109Cascades (Constant Pressure)
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1. Is this the best way to get the desired purity?
2. What am I going to do with streams L2, L1, V 4, V 5?
110Composition of intermediate streams
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z
33 , yV
33 , x L22 , yV
11, yV 22 , x L
11, x L
44 , x L
55 , x L
44 , yV
55 , yV
1. Is the composition of V 4and L
2 similar to that of the feed?
2. Is the composition of V 3 and L1 similar?
3. Is the composition of V 5 and L3 similar?
111Feed the intermediate streams back to the flash drums
yV
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z F ,
33, yV
22 , yV
11, yV
33 , x L
22 , x L
11, x L
44 , yV
55 , yV
44 , x L
55 , x L
3T
2T
54321 T T T T T
1T
4T
5T
1. How many “Heat Exchangers” do we
have and how many “Flash Drums” do
we have?
2. Is this energetically efficient?
3. How about the size of each flash drum?
112Adding reflux and boilup and combining the heat exchangers
yV
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z F ,
33 , yV
22 , yV
11, yV
33 , x L
22 , x L
11, x L
44 , yV
55 , yV
44 , x L
55 , x L
3T
2T
54321 T T T T T
1
T
4T
5
T
D0 L
B6V
Do we really need the “heat exchangers”?
113Let the heat and mass exchange happen simultaneously …
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The two streams L4 and V 5 are exchanging “heat” and “mass” with each other
Why not let them do it at the same time?
114From Cascades to Distillation Column
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D0 L
55 , x L
B6V
5T
4T
3T
2T
1T
44 , x L
33 , x L
22 , x L
11, x L
55 , yV
44 , yV
33 , yV
22 , yV
11, yV
z F ,
R
S/E
1. Link for Distillation Video1 – Steady State Operation
2. Link for Distillation Video2 – Startup
3. Lab scale Distillation Column Now we have only one reboiler
and one condenser!
115
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Designing a Binary Distillation Column
Problem Statement:
116
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Problem Statement:
I have a feed mixture of components “ A” and “ B” with a composition “ z ”
and I want to separate them to a desired composition
How many stages do I need?
What should be my feed location?
How much is the heat load on my reboiler and condenser?
Which equations do I have?
Material Balance
Energy Balance
Vapor – Liquid Equilibrium Data
117Overall Mass and Energy Balance on a Distillation Column
Q
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D D H x D ,,0 L
B B H x B ,,
F F T H z F ,,, D
L R 0
C Q
RQ
D B
DH BH QQ FH
Dx Bx Fz
D B F
D B RC F
D B
,calculatecanwe
specified,isseparation
of degreetheIf
columnon the balance
EnergyandMaterial
118How to calculate heat load?
QHV
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condenserthearound balance
EnergyandMaterialWriting
D D H x D ,,0 L
B B H x B ,,
D
L R 0
C Q
RQ
11, H V
1
110
01101
1
However,
1
and
H H x x
x z F RQ
x x
x z F D
Fx x x D
x D F Dx Bx Dx Fz
H H R D H H D LQ
H D LQ H V D LV
D
B D
Bc
B D
B
B B D
B D B D
D DC
DC
Designing a Binary Distillation Column 119
M t i l B l E b l
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D0 L
B
z F ,
Material Balances, Energy balances
and Equilibrium Relations:
Rectification section
Feed Tray
Stripping or Exhausting Section
Rectification section – Lets start from the first tray … 120
BalancesMaterialWritingQ
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D0 L
11 x L 22 yV
11, y x
5Equations
5and,,,areUnknowns
equations2,Components2
RelationsmEquilibriu,,,
BalanceEnergyWriting
and
12221
1111112222
112212
LV T y x
T xh L x Dh yT QT y H V
Dx x L yV D LV
D DC
D
C Q
5Equations
5and,,,areUnknowns
equations2,Components2RelationsmEquilibriu
,,,
BalanceEnergyWriting
and
BalancesMaterialWriting
23332
2222113333
223323
LV T y x
T xh L x Dh yT QT y H V
Dx x L yV D LV
D DC
D
D0 L
22 , y x
C Q
22 x L 33 yV
Rectification section – General set of equations 121
BalancesMaterialWriting
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5Equations
5and,,,areUnknowns
equations2,Components2
RelationsmEquilibriu
,,,
BalanceEnergyWriting
and
BalancesMaterialWriting
111
111111
111
j j j j j
j j j j D DC j j j j
D j j j j j j
LV T y x
T xh L x Dh yT QT y H V
Dx x L yV D LV
Can we write a similar set of equations for the stripping section?
Stripping section – General set of equations 122
BalancesMaterialWriting
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5Equations
5and,,,areUnknowns
equations2,Components2
RelationsmEquilibriu
,,
BalanceEnergyWriting
and
BalancesMaterialWriting
11
1111
111
k k k k k
B Bk k k k Rk k k k
Bk k k k k k
LV T y x
x BhT xh LQT y H V
Bx x L yV B LV
Bk k y x ,
RQ
11 k k x L k k yV
How do we know Q R ?
Is the partial reboiler like an additional distillation stage?
1nV
Operating line for the stripping and rectification section 123
What is an “operating line” ?
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p g
A quick recap of our flash calculations
An (x,y ) line on which all the points satisfy the material balanceequations
B
k
k k
k
k k
D
j
j
j
j
j
j
x
V
L x
V
L y
xV
L
xV
L
y
1
sectionstrippingfor thelineOperating
1
sectionionrectificatfor thelineOperating
11
1
11
1
What is the slope of the
“operating line” ? +ve
or – ve?
Where do they
intersect the x = y
diagonal?
What is the difference between this “operating line” and the one we saw during the
single stage flash calculation? Are x j and y j +1 in equilibrium with each other?
Lets visualize it graphically … 124
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x
y
12
12
2
1
and betweenRelation
1Slope
1TrayforlineOperating
x y
D LV V
L
D x
11, y x
21, y x22
, y x
23
23
3
2
and betweenRelation
1Slope
2TrayforlineOperating
x y
D LV V
L
32 , y x
Constant Molal Overflow (CMO) Approximation 125
How can we have a single straight line as our “operating line” for the
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rectification (and stripping) section?
sectionStripping
sectionionRectificat
1
1
21
21
V V V V
L L L L
V V V V
L L L L
k f f
k f f
j
j
Bk k
D j j
xV
L x
V
L y
xV
L x
V
L y
1
sectionstrippingfor thelineOperating
1
sectionionrectificatfor thelineOperating
1
1
Underlying assumption behind CMO 126
11222233 and DxxLyVDxxLyV
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11 x L 22 yV
22 x L 33 yV
32
32
21
21
32
2122331122
23
12
2123
11222233
get,we balanceenergythefromAnd
thenandIf
and
y y
H H
x x
hh
H H hh
LV h L H V h L H V
y y
x x
L
V
L LV V
Dx x L yV Dx x L yV D D
The slopes of the liquid and vapor enthalpy lines are equal! They are parallel!
The latent heat does not depend on composition!
CMO Operating line in terms of reflux ratio 127
The operating line equations can also be written in terms of reflux ratio (R ) and
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Boilup ratio (V B )
B
B
k
B
Bk
B
B B
D j j
xV
xV
V y
V
V
V
L B LV
B
V V
x R
x R
R y
R
R
V
L
D LV D
L
R
11
sectionstrippingfor thelineOperating
1 and
1
1
1
sectionionrectificatfor thelineOperating
1 and
1
1
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Rectification Section (total condenser) 129
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x
y
B x
1, n B y x1, nn y x
nn y x ,
nn y x ,1
Combining the rectification and stripping sections 130
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x
y
Where do you think the two lines (A, B or C) should intersect and why?
A
B
C
feed z
Equation for the feed line 131
L V
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L V
LV
F
z F L L F F
F F x F F F L L
F L L y
F
Fz x L L yV V
F L LV V V L LV F
get,we byrdenominatoandnumeratorthedivingandtwotheCombining
get,we balancecomponenttheFrom
gettray wefeedon theBalanceMaterialtheFrom
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Feed Quality 133
L L L f V
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L V
L V
F
liquidsubcooled1
q
F L L
L V
L V
F
point bubbleatliquid1
q
F L L
L V
L V
F
feedvaporized partially10
q
F L L
f L
L V
L V
F
pointdewatVapors0
q
L L
f V L V
L V
F
VaporsdSuperheate0
q
L L
f V
Feed Line on the plot 134
= 1
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x
y z (Saturated Vapor) q=0
( S a t u r a t e d
L i q u i d ) q =
Where to introduce the feed? 135
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x
y
Feed introduced here –
Below the optimum stage
No. of Stages Required = 7
D x B x
Where to introduce the feed? 136
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x
y
Feed introduced here –
Above the optimum stage
No. of Stages Required = 7
D x B x
Where to introduce the feed? 137
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x
y
Feed introduced here –
At the optimum stage
No. of Stages Required = 5
D x B x
Limiting Cases – Total Reflux (Minimum No. of Stages) 138
0 D B F
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1thenIf
11
sectionstripping
for thelineOperating
1thenIf
1
1
1
sectionionrectificat
for thelineOperating
1
1
slopeV
xV xV
V
y
slope R
x R
x R
R y
B
B B
k B
B
k
D j j
x
y
No. of Stages Required = 4
D x B x
Limiting Cases – Minimum Reflux (Infinite No. of Stages) 139
linesoperatingtwoThe
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separationdesiredthe
achievetorequiredare
stagesof numberInfinite
curvemequilibriu
on theintersect
p g
x
y
No. of Stages Required = ∞
D x B x
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Open Steam Distillation 141
CQ For separations involving a
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D
D
H
x D ,,
0 L
B B H x B ,,
F F T H z F ,,, D
L R 0
C
s H S ,
mixture of a light component
(ex.methanol) and water.
Since the bottom product is rich
in less volatile component
(water), instead of partially
reboiling water ( with a bit of
methanol), lets supply pure
water vapors.
How will the overall balance change?
How will the tray-balance change?
Open Steam Distillation 142
C Q EnergyandMaterial
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D
D
H
x D ,,
0 L
B B H x B ,,
F F T H z F ,,, D
L R 0
s H S ,lculate)tables/ca(steam
steamof enthalpytheis
late)data/calcu(enthalpy
obtained becan
andn,compositio product
bottomandtoptheknowweIf
(3)
(2) (1)
columnon the balance
S
D B
D BS C F
D B
H
H H
DH BH SH Q FH
Dx Bx Fz D BS F
Can we solve the material balance independently?
If reflux ratio is specified… 143
EnergyandMaterialWritingC Q11, H V
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condenserthearound balance
EnergyandMaterialWriting
D D H x D ,,0 L
B B H x B ,,
D
L R 0
RQ
coupledare balancesEnergyandMaterial
(5)and(2)(1),equations;3and
and,unknowns;threehaveonlyWe
(5) 1
(3),eq.in(4)ngSubstituti
(4) 1
and
1
110
01101
D BS
DH BH H H R DSH FH
H H R D H H D LQ
H D LQ H V D LV
D B DS F
D DC
DC
Internal Balances (Rectification section and Feed line) 144
C Q Is the rectification section of
di ill i l
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0 L
B B H x B ,,
F F T H z F ,,, D
L R 0
s H S ,
“Open Steam” distillation column
any different?
Does the feed tray look any
different?
D j j xV
L x
V
L y
1
sectionionrectificatfor thelineOperating
ion,approximatCMOUnder
1
1
1
1
linefeedfor thelineOperating
z q
xq
q y
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Operating lines for Open Steam Distillation 146
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x
y
D x B x
sectionionRectificatV
LSlope
1forlineFeed q
sectionStrippingV
L
Slope
B x x- asinterceptanhaslineOperating
diagonal.intersectnotdoeslineOperating B
Bk k
x x y
xV
L x
V
L y
,0atHence
1
Multiple feed streams 147
C Q How many operating lines will be
h i hi di ill i l ?
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D x D,0 L
B x B,
11, z F
RQ
22 , z F
there in this distillation column?
Multiple feed streams 148
C Qion,approximatCMOUnder
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D x D,0 L
B x B,
11, z F
RQ
22 , z F
tion
j
tion
tion
D j
D j j
V
x
V
L y
V
Dx x
V
L
xV
L x
V
L y
secsec
sec
11
1
1
1
1
11
1
1SectionforlineOperating
1
2
3
11, LV
22 , LV
33 , LV
Multiple feed streams 149
C Qion,approximatCMOUnder
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D x D,0 L
B x B,
11, z F
RQ
22 , z F
3
2211
3
3
2
11
2
2
11
1
3Section
2Section
1Section
V
z F z F Dx xV
L y
V
z F Dx x
V
L y
V
Dx x
V
L y
D
D
D
1
2
3
11, LV
22 , LV
33 , LV
Multiple feed streams: McCabe – Thiele Method 150
Find x D on the diagonal and draw the
operating line for section–1
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operating line for section – 1.
Feed characteristics are given and you
can draw the feed line for F 1 andoperating line for section – 1 intersects
the feed line.
Material balance on feed tray for F 1 and
calculate L2 and V 2 (know the slope).
Draw the operating line for section – 2. Feed characteristics are given and you
can draw the feed line for F 2 and
operating line for section – 2 intersects
the feed line.
Operating line for section – 3 will pass
through x B. x
y
D
x B
x
1forlineFeed F
1Section
2forlineFeed F
2Section
3Section
1 z 2 z
Side stream 151
C Q Will the operating lines look the
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D x D,0 L
B x B,
S xS ,
RQ
z F ,
same as those of Multiple feed
streams?
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153
C Q
Side stream
ion,approximatCMOUnder
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D x D,0 L
B x B,
RQ
z F ,
1
2
3
11, LV
22 , LV
33 , LV
S xS ,
33
3
22
2
11
1
3Section
2Section
1Section
V
Fz Sx Dx xV
L y
V
Sx Dx x
V
L y
V
Dx x
V
L y
S D
S D
D
Side stream: McCabe – Thiele Method 154
Find x D on the diagonal and draw the
operating line for section–1.
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operating line for section 1.
Calculate the slope of the operating line
for section – 2 (slope less than theoperating line for section – 1). You can
draw the “pseudo-feed line”. You can
also calculate the y – intercept.
Feed characteristics are given and you
can draw the feed line for F 2 andoperating line for section – 2 intersects
the feed line.
Operating line for section – 3 will pass
through x B.
The last stage in section – 1 has to end at
the intersection of operating lines of
section 1 and section 2
x
y
D
x B x
1Section
2forlineFeed F
2Section
3Section
S x z